Offline. Put the wallet .dat files on a usb stick and keep them safe.
The wallet must have never been on a computer that has connections to the internet before. Doing so may result in your private key being compromised in the event that there is a virus infection.
No it doesn't. All you need is to make sure your computer is safe. If you use a computer that is only ever used for bitcoin transactions then there likely isn't going to be any issues.